Question

Y^2=n^2+5n ; Find K(2)
Answer should be +-square root of 14

Answer 1

Can you simplify this format again please sorry just shorten it a but

Answer 2

To solve the equation \( Y^2 = n^2 + 5n \) and find \( K(2) \), we first rewrite the equation in a more useful form for identifying solutions.

We can express \( Y^2 \) as follows:

\[
Y^2 = n^2 + 5n
\]

This is a quadratic equation in terms of \( n \):

\[
Y^2 = n(n + 5)
\]

To find \( K(2) \), we will substitute \( n = 2 \):

\[
Y^2 = 2(2 + 5) = 2 \times 7 = 14
\]

Thus,

\[
Y^2 = 14
\]

To find \( Y \), we take the square root of both sides:

\[
Y = \pm \sqrt{14}
\]

Therefore, we have:

\[
K(2) = \pm \sqrt{14}
\]

Thus, the answer is:

\[
\boxed{\pm \sqrt{14}}
\]

Answer 3

Certainly!

To find \( K(2) \) for the equation \( Y^2 = n^2 + 5n \):

1. Substitute \( n = 2 \):
\[
Y^2 = 2^2 + 5 \cdot 2 = 4 + 10 = 14
\]

2. Take the square root:
\[
Y = \pm \sqrt{14}
\]

So, \( K(2) = \pm \sqrt{14} \).

Final answer:
\[
\boxed{\pm \sqrt{14}}
\]